1. A Company that operates 10 hours a day and manufactures two products on three sequential
processes . The following table summarizes the data of the problem. Determine the optimal
mix of two products.
Minutes per Unit
Product Process Process Process
Unit
1
2
3
Profit
1
10
6
8
$2
2
5
20
10
$3
2. Show and Sell Company can advertise ist products, on local radio and television. The
advertising budget is is limited to $10,000 a month. Each minute of radio advertising costs
$15 and each minute of TV commercials $300. The Company likes to advertise on radio at
least twice as much as on TV. In the meantime , it is not practical to use more than 400
minutes of radio advertising a month. From past experience , advertising on TV is estimated
to be 25 times as effective as on radio. Determine the optimal allocation of budget to radio
and TV advertising.
3. A fast moving consumer good company produces tomato in 3 factories and sells the products
via 4 distributors in different regions. Below you can find monthly capacities of factories and
demands of distributors and unit transportation cost from a factory to a distributor.
Construct the model.
Factory
Capacity(pcs./month)
A
400,000
B
240,000
C
360,000
total
1,000,000
Distributor
A
B
C
D
Total
Demand(ton/month)
200,000
280,000
350,000
130,000
960,000
Dist./Factory
1
2
3
1
22
19
36
2
40
35
12
3
32
20
18
4
20
38
34
4. Consider the following LP :
Max Z = 2X1+3X2
X1+3X2 ≤ 6
3X1+2X2 ≤ 6
X1,X2 ≥ 0
a. Determine all the basic solutions of the problem , and classify them as feasible and
infeasible.
5. Below given two type of products and activities in a logistics center. Handling of these two
type of products have different profit income. The managers want to increase the capacity of
first activity (Collecting).
a. Make a working plan for this logistics center.
b. If the managers want to increase capacity, which function’s capacity would be
increase?
Product 1
Product 2
Capacity(weekly)
Collecting
5 hour
4 hour
24 hour
Loading
2 hour
5 hour
13 hour
Profit
7,000
10,000
-
6. Write the dual for each of the primal problems.
a.
Max Z =-5X1+2X2
-X1+X2 ≤ 2
2X1+3X2 ≤ 5
X1, X2 ≥ 0
b.
Min Z =6X1+3X2
6X1-3X2+ X3 ≥2
3X1+4X2+ X3 ≥5
X1, X2 , X3 ≥ 0
7.


Min 12X1 + 10X2 + 15X3 + 11X4 - 22X5
3X1
- 6X3 + 7X4
= 21
X1 + 3X2
- 2X4 + 5X5 = 14
2X1 + 4X2 + 5X3
- 3X5 = 17
X1 , X2 , X3 , X4 , X5 ≥ 0
Write down the dual model.
Determine if the solution below is optimal or not? (X1=0 X2=5 X3=0 X4=3 X5=1) (y1=1 y2=-2 y3= 4)